Spin module versions of Weyl's reciprocity theorem for classical Kac- Moody Lie algebras. An application to branching rule duality

DOI10.2977/prims/1195172705zbMath0699.17020OpenAlexW2046267298MaRDI QIDQ912964

Kohji Hasegawa

Publication date: 1989

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195172705

zbMATH Keywords

Young diagramsdual pairsspin modulesKac-Moody Lie algebrasbranching rule dualityFermion Fock space representationsNeveu-SchwarzRamondS-transformation rule duality

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items

Crystal graphs for Lie superalgebras and Cauchy decomposition, A level-rank duality for parafermion vertex operator algebras of type A, Quasi-Galois symmetries of the modular \(S\)-matrix, Infrared phases of \(2d\) QCD, Chern-Simons-matter dualities with SO and USp gauge groups, L-operator for Belavin’s R-matrix acting on the space of theta functions, On centralizer algebras for spin representations, Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras., Lie algebra cohomology and \(N=2\) SCFT based on the GKO construction, Quasi-finite modules for Lie superalgebras of infinite rank, Level-rank duality of WZW models in conformal field theory, A Robinson-Schensted-type correspondence for a dual pair on spinors, Reflection and algorithm proofs of some more Lie group dual pair identities, Pursuing the double affine Grassmannian. I: Transversal slices via instantons on \(A_k\)-singularities, Rank-level duality of conformal blocks for odd orthogonal Lie algebras in genus $0$, M-theoretic derivations of 4d-2d dualities: from a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems, Exact solutions of 2d supersymmetric gauge theories, Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions, Generalized theta functions, strange duality, and odd orthogonal bundles on curves

Cites Work

• Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Unitary representations of the Virasoro and super-Virasoro algebras
• Classical affine algebras
• Unitary representations of the Virasoro algebra
• Young-diagrammatic methods for the representation theory of the classical groups of type \(B_ n\), \(C_ n\), \(D_ n\)
• Dual pairs on spinors. Cases of \((C_ m,C_ n)\) and \((C_ m^{(1)},C_ n^{(1)})\)
• Geometric realization of conformal field theory on Riemann surfaces
• Modular and conformal invariance constraints in representation theory of affine algebras
• Sugawara operators and Kac-Kazhdan conjecture
• Structure of representations with highest weight of infinite-dimensional Lie algebras
• Basic representations of affine Lie algebras and dual resonance models
• On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
• Dirac operator and the discrete series
• Transcending Classical Invariant Theory
• Spinor representations of affine Lie algebras
• Spin and wedge representations of infinite-dimensional Lie algebras and groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item